Mälardalen University Doctoral Dissertation 293 Karl Lundengård Lundengård Karl Extreme points of the Vandermonde determinant and phenomenological EXTREME POINTS OF THE VANDERMONDE DETERMINANT AND PHENOMENOLOGICAL MODELLING WITH POWER EXPONENTIAL FUNCTIONS modelling with power exponential functions Karl Lundengård Address: P.O. Box 883, SE-721 23 Västerås. Sweden ISBN 978-91-7485-431-2 Address: P.O. Box 325, SE-631 05 Eskilstuna. Sweden E-mail:
[email protected] Web: www.mdh.se ISSN 1651-4238 2019 1 Mälardalen University Press Dissertations No. 293 EXTREME POINTS OF THE VANDERMONDE DETERMINANT AND PHENOMENOLOGICAL MODELLING WITH POWER EXPONENTIAL FUNCTIONS Karl Lundengård 2019 School of Education, Culture and Communication 2 Copyright © Karl Lundengård, 2019 ISBN 978-91-7485-431-2 ISSN 1651-4238 Printed by E-Print AB, Stockholm, Sweden 3 Mälardalen University Press Dissertations No. 293 EXTREME POINTS OF THE VANDERMONDE DETERMINANT AND PHENOMENOLOGICAL MODELLING WITH POWER EXPONENTIAL FUNCTIONS Karl Lundengård Akademisk avhandling som för avläggande av filosofie doktorsexamen i matematik/tillämpad matematik vid Akademin för utbildning, kultur och kommunikation kommer att offentligen försvaras torsdagen den 26 september 2019, 13.15 i Delta, Mälardalens högskola, Västerås. Fakultetsopponent: Professor Palle Jorgensen, University of Iowa Akademin för utbildning, kultur och kommunikation 4 Abstract This thesis discusses two topics, finding the extreme points of the Vandermonde determinant on various surfaces and phenomenological modelling using power-exponential functions. The relation between these two problems is that they are both related to methods for curve-fitting. Two applications of the mathematical models and methods are also discussed, modelling of electrostatic discharge currents for use in electromagnetic compatibility and modelling of mortality rates for humans.